# Worldwide Differential Equations with Linear Algebra 1st edition

Robert McOwen
Publisher: Worldwide Center of Mathematics

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• Chapter 1: First-Order Differential Equations
• 1.1: Differential Equations and Mathematical Models (8)
• 1.2: Geometric Analysis and Existence/Uniqueness (6)
• 1.3: Separable Equations & Applications (16)
• 1.4: Linear Equations & Applications (12)
• 1.5: Other Methods (10)

• Chapter 2: Second-Order Differential Equations
• 2.1: Introduction to Higher-Order Equations (8)
• 2.2: General Solutions for Higher-Order Equations (8)
• 2.3: Homogeneous Equations with Constant Coefficients (14)
• 2.4: Free Mechanical Vibrations (12)
• 2.5: Nonhomogeneous Equations with Constant Coefficients (10)
• 2.6: Forced Mechanical Vibrations (11)
• 2.7: Electrical Circuits (7)

• Chapter 3: Laplace Transform
• 3.1: Laplace Transform and Its Inverse (23)
• 3.2: Transforms of Derivatives, Initial-Value Problems (13)
• 3.3: Shifting Theorems (22)
• 3.4: Discontinuous Inputs (16)
• 3.5: Convolutions (13)

• Chapter 4: Systems of Linear Equations and Matrices
• 4.1: Introduction to Systems and Matrices (10)
• 4.2: Gaussian Elimination (16)
• 4.3: Reduced Row-Echelon Form and Rank (16)
• 4.4: Inverse of a Square Matrix (14)
• 4.5: The Determinant of a Square Matrix (9)
• 4.6: Cofactor Expansions (10)

• Chapter 5: Vector Spaces
• 5.1: Vectors in Rn (9)
• 5.2: General Vector Spaces (7)
• 5.3: Subspaces and Spanning Sets (20)
• 5.4: Linear Independence (8)
• 5.5: Bases and Dimension (13)
• 5.6: Row and Column Spaces (6)
• 5.7: Inner Products and Orthogonality (6)

• Chapter 6: Linear Transformations and Eigenvalues
• 6.1: Introduction to Transformations and Eigenvalues (10)
• 6.2: Diagonalization and Similarity (13)
• 6.3: Symmetric and Orthogonal Matrices (9)

• Chapter 7: Systems of First-Order Equations
• 7.1: Introduction to First-Order Systems (12)
• 7.2: Theory of First-Order Linear Systems (20)
• 7.3: Eigenvalue Method for Homogenous Systems (14)
• 7.4: Applications to Multiple Tank Mixing (2)
• 7.5: Applications to Mechanical Vibrations (5)

• A: Complex Numbers
• B: Review of Partial Fractions
• C: Table of Integrals
• D: Table of Laplace Transforms
• E: Answers to Some Exercises
Worldwide Differential Equations with Linear Algebra, 1st edition is designed for a one-semester undergraduate course in ordinary differential equations and linear algebra. This text adopts a concise writing style and careful selection of topics to keep the book shorter than many others on this subject. The WebAssign component to this textbook provides students with immediate feedback, videos of worked problems, and a searchable eBook.

## Features

• Select questions contain links to videos of the worked problem, ideal for visual learners.

## Questions Available within WebAssign

Most questions from this textbook are available in WebAssign. The online questions are identical to the textbook questions except for minor wording changes necessary for Web use. Whenever possible, variables, numbers, or words have been randomized so that each student receives a unique version of the question. This list is updated nightly.

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Group Quantity Questions
Chapter 1: First-Order Differential Equations
1.1 8 001a 001b 001c 002b 002c 002d 003 004
1.2 6 001 002b 002c 003b 003c 003d
1.3 16 001b 001c 001d 001e 001f 002a 002b 002c 004 005 006 007 008 010 011 013
1.4 12 001a 001b 001d 001f 002a 002b 002c 002d 002e 003 005 007
1.5 10 001b 001c 001d 002a 003b 003c 003d 004a 004b 004c
1.6 17 002 003 004 005 006 007 008 009 013 015 016 017 019 020 022 023 024
Chapter 2: Second-Order Differential Equations
2.1 8 001b 001d 002a 002b 002c 002d 004 005
2.2 8 001 003 004 006 007 010 011 012
2.3 14 002a 002b 002c 002d 002e 002f 002g 002h 003a 003b 003c 003d 003e 003f
2.4 12 001 002 003 004 005 006b 006c 006d 006e 007a 007b 009
2.5 10 001a 001b 001c 001d 001e 001f 002a 002b 002c 002d
2.6 11 001 002 003a 003b 006a 006b 006c 007a 007b 008a 008b
2.7 7 003a 003b 003c 004a 004b 004c 004d
2.8 8 001 002 003 005 006 008 009 010
Chapter 3: Laplace Transform
3.1 23 004a 004b 004c 004d 004e 005a 005b 005c 005d 005e 005f 005g 005h 006a 006b 006c 006d 006e 006f 007a 007b 007c 007d
3.2 13 002a 002b 002c 003a 003b 003c 003d 004 005 006a 006b 006c 006d
3.3 22 001a 001b 001c 001d 001e 001f 002a 002b 002c 002d 003a 003b 003c 004a 004b 004c 005a 005b 006a 006b 007 008
3.4 16 001a 001b 002a 002b 003a 003b 003c 003d 004a 004b 005a 005b 005c 005d 006 008
3.5 13 001a 001b 001c 001d 002a 002b 002c 003a 003b 003c 004a 004b 004c
3.6 3 001 005 010
Chapter 4: Systems of Linear Equations and Matrices
4.1 10 001a 001b 001d 002 003a 003b 003c 003d 004 005
4.2 16 001a 001c 002a 002b 002c 002d 003a 003b 003c 003d 004a 004b 004c 004d 005a 005b
4.3 16 001c 001d 002a 002b 002c 002d 002e 002f 004a 004b 004c 004d 005a 005b 005c 005d
4.4 14 004a 004b 004c 004d 004e 004f 005a 005b 005c 005d 006a 006b 006c 006d
4.5 9 001a 001b 001c 001d 002a 003a 003b 004a 004b
4.6 10 001a 001b 001c 001d 001f 002a 002b 002c 003a 003b
4.7 16 003 005 011 013 014 015 016 017 018 019 021 022 023 024 027 028
Chapter 5: Vector Spaces
5.1 9 001 002 003 004 005 006 007 008 009
5.2 7 003a 003b 003c 003d 003e 003f 003g
5.3 20 001a 001b 001c 002a 002b 002c 002d 003a 003b 003d 004a 004b 004c 004d 005a 005b 006a 006c 006d 007a
5.4 8 001a 001b 001c 001d 001f 002a 002b 002c
5.5 13 001a 001b 001c 001d 001e 003a 003b 003c 003d 004a 004b 004c 004d
5.6 6 001a 001b 001c 002a 002b 002c
5.7 6 004a 004b 004c 005a 005b 005c
5.8 4 009b 009c 013 019
Chapter 6: Linear Transformations and Eigenvalues
6.1 10 001a 001b 001c 001d 001e 001f 002a 002b 002c 004
6.2 13 001a 001b 001c 001e 002a 002b 002c 003a 003b 003c 004a 004b 004c
6.3 9 001a 001c 001d 002a 002c 003a 003b 003c 006
6.4 1 001a
Chapter 7: Systems of First-Order Equations
7.1 12 001a 001b 001c 001d 002a 002b 002c 002d 003a 003b 003c 003d
7.2 20 001a 001b 001c 001d 002a 002b 002c 002d 003a 003b 003c 003d 004a 004b 004c 004d 005a 005b 005c 005d
7.3 14 001a 001b 001c 001d 002a 002b 002c 002d 003a 003b 004a 004b 004c 004d
7.4 2 001 003
7.5 5 001 004 006 008 009
7.6 4 007 008 009 010
Total 491